Context. Analysis of all-sky Planck submillimetre observations and the IRAS 100 mu m data has led to the detection of a population of Galactic cold clumps. The clumps can be used to study star formation and dust properties in a wide range of Galactic environments.

Aims. Our aim is to measure dust spectral energy distribution ( SED) variations as a function of the spatial scale and the wavelength.

Methods. We examined the SEDs at large scales using IRAS, Planck, and Herschel data. At smaller scales, we compared JCMT/SCUBA-2 850 mu m maps with Herschel data that were filtered using the SCUBA-2 pipeline. Clumps were extracted using the Fellwalker method, and their spectra were modelled as modified blackbody functions.

Results. According to IRAS and Planck data, most fields have dust colour temperatures T-C similar to 14-18K and opacity spectral index values of beta = 1.5-1.9. The clumps and cores identified in SCUBA-2 maps have T similar to 13K and similar beta values. There are some indications of the dust emission spectrum becoming flatter at wavelengths longer than 500 mu m. In fits involving Planck data, the significance is limited by the uncertainty of the corrections for CO line contamination. The fits to the SPIRE data give a median beta value that is slightly above 1.8. In the joint SPIRE and SCUBA-2 850 mu m fits, the value decreases to beta similar to 1.6. Most of the observed T-beta anticorrelation can be explained by noise.

Conclusions. The typical submillimetre opacity spectral index fi of cold clumps is found to be similar to 1.7. This is above the values of diffuse clouds, but lower than in some previous studies of dense clumps. There is only tentative evidence of a T-beta anticorrelation and beta decreasing at millimetre wavelengths.